I just don't know. I'd really rather go with a smaller (physically) build for portability, but if the second build is a lot stronger, I might be persuaded to sacrifice size and a few hundred bucks. What do you think? Noticable difference or what?

Both look about the same, the biggest gaming factor will be the video card and both are using the a 1060, which is fine @1080.

Unless you have a case and psu already for the mini build, you are missing those in the build. Also, on the tower build you have a much larger hard drive. I do not think the costs are as far off as you think, probably about the same all in - case and PSU will about make up the difference.

The 8600k would be more powerful according to Passmark. Plus it has a higher turbo boost. The desktop build has a platter and I would upgrade that to a SSD of at least 256GB and then get a 1 TB platter as spill over. If you want portability, check out the case in my Sig. It has a handle at the top so you can easily take it to LAN parties or what ever. The handle has come in mighty handy for me personally since I had to move my desktop to my work bench so many times to do things in my computer. Like upgrade RAM, video card and install and mess around with a fan controller.

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Note that Ryzen 2600 comes out in 3 days so would go that route over the 1600. Honestly unless you're trying to dig through benchmarks either the 1600/2600 or the 8600K is going to do just fine for you. If you're wanting to overclock get the 8600K since it'll go higher but if not something you intend to mess with then a 2600X would be a better route in the long run since it's multi threaded and has a better stock cooler.

I decided to downgrade on the GPU and just wait till general prices come down (hopefully). I may go with a 1060 3GB (non ti) which seems to go for about $250 when you can get a deal. But even with the 1050 ti 4GB I can play new games like Far Cry 5 on Medium, which isn't too bad.

I would get a better processor, but by the time I do that, and then get the slightly better GPU, I'm out another $100. I'm trying to cut costs. As you can see, there's no case there. That's because I'm going to build a semi open case out of wood and glass. Shipping costs for me are $10 a pound, so I'm saving about $100-100+ on the case. The CPU cooler is actually going for $60 on Amazon right now.